Real-time open-hole wireline sonic logging data processing becomes a nontrivial task to accurately, automatically, and efficiently evaluate the compressional and shear slowness of a borehole rock formation when human interaction is not possible and the signal processing time is limited to the elapsed time between different transmitter excitations. To address real-time sonic data processing challenges, we have developed self-adaptive, data-driven methods to accurately measure the formation P- and S-wave slowness from monopole and dipole waveforms in all types of formations. These new real-time processing techniques take advantage of the fact that advanced wireline sonic logging tools have wide frequency responses and little to no detectable tool body arrivals. These technology improvements provide an opportunity to implement a first-motion-detection technique that detects the onset of P-waves in the monopole array waveforms. The knowledge of compressional arrival time and corresponding slowness are then used to project an appropriate slowness-time window to identify the monopole refracted S-wave and its slowness based on the range of possible compressional to shear velocity ratio (/) for earth rock formation. To process the borehole dipole flexural waves, we develop a new, data-driven frequency-domain method that enables the evaluation of the full flexural-wave dispersion response and its corresponding low-frequency shear slowness asymptote. Field data processing results indicate that our methods provide high-quality compressional slowness (delta-T compressional) and shear slowness measurements that are not affected by other borehole modes or dispersion complications in most formation types.